APY calculator
Banks quote two different numbers and only one of them tells you what you get paid. Enter the stated rate and how often it compounds to see the APY behind it.
That rate is an annual percentage yield of
4.081%
On a balance of $10,000.00 left alone for a year, that pays $408.08 in interest and leaves you with $10,408.08.
What APY actually measures
Annual percentage yield answers one question: if you put money in and left it alone for a year, what fraction of it would you get back as interest? It folds the compounding schedule into a single figure so you never have to think about the schedule again.
The interest rate on its own does not answer that question. A 4.00% rate that compounds daily and a 4.00% rate that compounds once a year pay different amounts, $408.08 and $400.00 on a $10,000 balance. Both banks can honestly advertise "4.00%" if they are quoting the nominal rate. Only the APY separates them.
The formula
APY = (1 + r/n)n minus 1, where r is the stated annual rate as a decimal and n is the number of compounding periods in a year.
Work the 4.00% daily case by hand. Divide 0.04 by 365 to get a daily rate of 0.0001096. Add one, raise to the power of 365, and you get 1.040808. Subtract one and you have 4.0808%. That is the number the bank must print.
How much the compounding schedule is worth
Not much, which is the useful conclusion. Here is a 4.00% stated rate on $10,000 across every schedule a US bank realistically uses.
| Compounding | APY | Interest in year one |
|---|---|---|
| Once a year | 4.0000% | $400.00 |
| Quarterly | 4.0604% | $406.04 |
| Monthly | 4.0742% | $407.42 |
| Daily | 4.0808% | $408.08 |
Eight dollars separates the best schedule from the worst. If you are choosing between two accounts and one compounds daily while the other compounds monthly, that is not the reason to pick either. Compare the published APYs and let the schedule sort itself out.
The mistake this page exists to prevent
If a bank gives you an APY, do not run it through this calculator to "add" compounding. The compounding is already in there. Doing it twice is the most common error in savings maths, and on a thirty-year projection it inflates a $10,000 balance by $701. The main savings calculator takes APY directly for exactly this reason.
Questions about APY
What is the difference between APY and interest rate?
The interest rate is the raw annual rate before compounding. APY is what you actually receive once compounding is counted. A 4.00% rate compounded daily works out to 4.0808% APY, so on $10,000 you receive $408.08 rather than $400. APY is the number to compare accounts on.
Is APY the same as APR?
No, and they point in opposite directions. APY describes what you earn on money you deposit and includes compounding. APR describes what you pay on money you borrow and includes fees but usually excludes compounding. Seeing APR on a savings product is a sign the disclosure is unusual, so read it carefully.
Why do banks advertise APY instead of the interest rate?
Because federal rules make them. The Truth in Savings Act and Regulation DD require deposit account disclosures to state the annual percentage yield, calculated a standard way, so that two accounts can be compared on one number. It is one of the few places in consumer finance where the comparison is genuinely apples to apples.
Does more frequent compounding earn much more?
Less than people expect. On a 4.00% stated rate, $10,000 earns $400.00 with annual compounding, $406.04 quarterly, $407.42 monthly, and $408.08 daily. The whole spread between yearly and daily is $8.08. Once you are comparing APYs, the compounding schedule is already priced in and you can ignore it.
How do I convert an APY back into an interest rate?
Take the APY as a decimal, add one, raise it to the power of one over the number of compounding periods, subtract one, then multiply by the number of periods. For a 4.0808% APY compounded daily, that returns 4.00%. The calculator above does this in reverse when you change the frequency.
Sources
- Consumer Financial Protection Bureau, Regulation DD (Truth in Savings) . Requires deposit accounts to disclose APY on a standard basis
- FDIC, National Rates and Rate Caps